with eyes open
With full knowledge or awareness. A noun or pronoun can be used between "with" and "eyes." "Wide" is often used before "open." If you don't sign this contract with eyes open, you're going to get yourself into trouble. Some guys forget to go out there with their eyes open, and they're the ones who end up getting hurt.
with one's eyes open
Fully aware, as in We started this project with our eyes open and are not surprised at the results. [First half of 1900s] Also see keep one's eyes open.